An electric generator converts mechanical energy into electrical energy. The generation of
alternating currents (ac) is based on the phenomenon of electromagnetic induction. A generator has a
coil wound on an armature which rotates in a magnetic field. See figure 17. A simple ac generator
consists of a rectangular coil mounted on a rotor shaft. It is rotated at a constant frequency in a uniform
magnetic field, B by external means. Such a
generator is shown in figure17. The axis of
rotation of the coil is perpendicular to the
direction of the magnetic field. Because of
rotation of the coil, the magnetic flux through
it changes and consequently an emf is induced
in the coil. The coil is connected to an external
circuit by means of slip rings and brushes.

If the coil rotates with an angular
velocity ω and initially (at t = 0) its plane is
perpendicular to the field (i.e. θ = 0^{0}), the
angle θ between the magnetic field vector
and the area vector of the coil at any instant
t is θ = ?t. The flux linked with the coil at time
t is given by Φ B = BA cos θ = BA cos ωt

If the coil has N turns, then the induced emf is given by

This is the instantaneous value of the emf. Here NBA ω is the maximum or peak value of the emf. It
can be denoted by ε_{0}. Thus,

where ω = 2 π f = 2 π / T and f is the frequency and T the time period of the revolution of generator coil.

Clearly, the
emf has its maximum
value at θ = 90^{0} (sin
90^{0} = + 1) or θ = 270^{0} (sin 270^{0} = - 1), as the
change of flux is
greatest at these
points. See figure 18.
It is also clear
that induced emf
varies sinusoidally with
time. Induced emf lags
behind the flux by π / 2 in phase. It means that when the flux is
maximum (i.e., the plane of the coil is perpendicular to the field),
the emf is zero and when the flux is zero (i.e., the plane of the coil is
parallel to the field), the emf is maximum. See figure 19.

The current so induced is called alternating current (ac) because its direction changes periodically.

In most of the commercial generators, the coils are held stationary and it is the electromagnets which are rotated. The frequency of rotation is 50 Hz in India (also the frequency of ac). In certain countries such as USA, it is 60 Hz.

CBSE Electromagnetic Induction ( With Hint / Solution)

Class XII (By Mr. Ashis Kumar Satapathy)

email - [email protected]

Electromagnetic Induction